Lange's 1938 Model
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Groupe de REcherche en Droit, Economie, Gestion UMR CNRS 7321 LANGE’S 1938 MODEL: DYNAMICS AND THE “OPTIMUM PROPENSITY TO CONSUME” Documents de travail GREDEG GREDEG Working Papers Series Michaël Assous Roberto Lampa GREDEG WP No. 2014-02 http://www.gredeg.cnrs.fr/working-papers.html Les opinions exprimées dans la série des Documents de travail GREDEG sont celles des auteurs et ne reflèlent pas nécessairement celles de l’institution. Les documents n’ont pas été soumis à un rapport formel et sont donc inclus dans cette série pour obtenir des commentaires et encourager la discussion. Les droits sur les documents appartiennent aux auteurs. The views expressed in the GREDEG Working Paper Series are those of the author(s) and do not necessarily reflect those of the institution. The Working Papers have not undergone formal review and approval. Such papers are included in this series to elicit feedback and to encourage debate. Copyright belongs to the author(s). Lange’s 1938 Model: Dynamics and the “Optimum propensity to consume” Michaël Assous* † Roberto Lampa‡ GREDEG Working Paper No. 2014-02 Introduction Oskar Lange’s 1938 work “The Rate of Interest and the Optimum Propensity to Consume” is widely recognized as one of the earliest mathematical models of Keynes’s General Theory. In light of its analytical content, it has usually been associated with the original IS-LM approach of Roy Harrod, James Meade and John Hicks (Young, 1987; Darity and Young, 1995). However, Lange’s article was not a reaction to Keynes’s works but the first part of an ambitious project that included the development of a theory of economic evolution1 (see Lampa 2013). Indeed, Lange manifested his interest in dynamics very early in his career (both his doctoral dissertation and his thesis presented for the ‘docent’ degree – i.e. assistant professor – were devoted to the analysis of the business cycle in Poland), repeatedly emphasizing the close connection between his view and Karl Marx’s ideas. Furthermore, he attached great importance also to the works of Joseph Schumpeter and Michal Kalecki2: from 1934 to 1936, he became tightly connected to the former at Harvard, whereas his interest in Kalecki’s business cycle seems to have grown more important after the publication of the General Theory3. * Corresponding author. Email: [email protected] † GREDEG (Groupement de Recherche en Droit, Economie et Gestion), Nice, France. Michael Assous benefited from support from the CNRS (GREDEG) and Duke University. ‡ CONICET (National Scientific and Technical Research Council) and University of Buenos Aires, Argentina 1 Although Lange explicitly suggested that his 1938 static model might have been dynamized, he never devised any mathematical demonstration: he just stated, en passant, that this might have been done by means of a time lag à la Kalecki4 (1937). It may be recalled, however, that in the early 1940s, Paul Samuelson devised some “techniques” in order to dynamize what he called the “Keynesian system” (1941: 113). As he explicitly affirmed in his 1941 Econometrica paper, “I shall analyze in some detail the simple Keynesian model as outlined in the General Theory. Various writers, such as Meade, Hicks, and Lange, have developed explicitly in mathematical form the meaning of the Keynesian system” (1941: 133). He then proceeded to develop two dynamic systems: both a differential and a difference set of equations and he presented the condition that assured the stability of the equilibrium (1941: 120). Although Samuelson explicitly referred to Lange, his models were only loosely related to his5. Firstly, Samuelson did not stress that the level of consumption was the key determinant of the investment function, as Lange repeatedly did. Secondly, and foremost, Samuelson paid no attention to the dynamics of the capital stock (which is the corner stone of Kalecki’s theory of fluctuations) to which Lange explicitly referred. On the other hand, it might also be remarked that Mabel Timlin (1942) made an attempt to dynamize what she had defined as the “Keynes-Lange” system. Her method mainly consisted of developing a “system of shifting equilibrium” to determine how a monetary shock was likely to induce a transformation in Lange’s set of structural functions, which were supposed to embed the “psychological-institutional complex” of the economy. Resorting to Lange’s diagrammatic representation, Timlin showed how expectations in both the goods and the financial market became critical elements with respect to the dynamics of the economy. Furthermore, by extending Lange’s analysis to the “long-run”, she was finally able to address the problem of the effects of a change in thriftiness upon the stationary level of the capital stock6. 2 Nevertheless, unlike Timlin and Samuelson, the present article focuses on Lange’s (crucial) notion of the “optimum propensity to consume”, whose importance is largely ignored in both the aforementioned analyses. In particular, the aim of this paper is to suggest a consistent reconstruction of Lange’s article in order to explore its potential implications in terms of dynamics. We are persuaded that such a reconstruction may be interesting from several perspectives. Firstly, it may help us to better understand how Lange’s notion of the “optimum propensity to consume” (on which he based his whole interpretation of the under-consumption theories) may operate in a dynamic context. Secondly and foremost, a similar reconstruction may be useful for making clear how close Lange’s view on dynamics – expressed in a series of articles published between 1934 and 1943 – was to the “Keynesian” dynamic approach of both Kalecki (1939) and Kaldor (1940) (according to Lange, the most prominent contributors of the late 1930s). Consequently, section 1 discusses Lange’s early reflection on dynamics with the aim of highlighting its most outstanding features. Section 2 focuses on Lange’s 1938 static model and indicates the effects of a change of saving on investment. Furthermore – by means of an unedited correspondence between Lange and Samuelson (dated 1942) recently discovered in the archives of Duke University by one of the authors – we clarify the meaning and the implications of the notion of “optimum propensity to consume”. Section 3, by means of some additional assumptions concerning the introduction of a time lag, outlines the necessary and sufficient conditions for the generation of self-sustaining cycles. Finally, Lange’s model (once dynamized) is compared to Kalecki’s 1939 business cycle theory, and its consistency with Lange’s view (expressed in a series of contemporary papers) is assessed. 1. The foundations of Lange’s endogenous dynamics: Marx and (a touch of) Schumpeter 3 According to a qualified judgement, the study of business cycles and the evolution of capitalism were Lange’s chief research concerns from his early youth until the end of the Second World War (Kowalik 2008). This notwithstanding (and paradoxically enough), Lange did not publish any work explicitly dealing with these issues in the aforementioned period7. However, it is possible to reconstruct the essentials of his reflection on dynamics by means of a careful re- reading of his main articles. In “Marxian Economics and Modern Economic Theory” (1935), Lange advocated for an approach that could explain the “economic evolution” from “within” the economic process. In this field, Modern Economic Theory was most likely to be misleading8. Lange’s argument was that by resorting to a static theory of equilibrium, “bourgeois economists” – that is, all the economists ranging from the Austrian, Marshallian and the Lausanne schools – were unable to depart from a framework in which all data related to preferences, institutions and technology are supposed to be given so that the only possible explanation to fluctuations and crises was an exogenous one. In Lange’s eye, this line of thought was likely to consolidate the unrealistic view that capitalist economies were intrinsically stable, whereas the 1930s contingency showed their destructive instability both in the United States and in Europe. Sarcastically enough, Lange wrote: “It was very generally held among “bourgeois” economists both at the beginning of the twentieth century and in the years preceding 1929, that the economic stability of Capitalism was increasing and that business fluctuations were becoming less and less intense. Thus the Marxian claim that “bourgeois” economists failed to grasp the fundamental tendencies of the evolution of the Capitalist system proves to be true.” (Lange, 1935: 190) However, it must bemarked that the “real” superiority of Marxian economics was not supposed to stem from any specific analytical tool originally used by Marx. Firstly, Lange considered that the labour theory of value, at best, can explain equilibrium’s price and production, once a given 4 amount of labour necessary to produce a commodity is known. On the other hand, it is of no use to highlight how changes (particularly, technological changes) occur. (Lange 1935: 194) Secondly, he thought that also the original version of Marx’s schemes of reproduction were of little help in the field of business cycle, because of its analytical backwardness9: “The inability of Marxian economics to solve the problem of the business cycle is demonstrated by the considerable Marxist literature concerned with the famous reproduction schemes of the second volume of Das Kapital. This whole literature tries to solve the fundamental problems of economic equilibrium and disequilibrium without even attempting to make use of the mathematical concept of functional relationship.” (Lange 1935: 196) The alleged superiority of Marxian economics laid instead on the exact specification of the institutional datum within which the economic process was studied. Its merit, in particular, was to study the functioning of an economy made of two main social classes: “[…] the consequences of the additional institutional' datum which distinguishes Capitalism from other forms of exchange economy, i.e. the existence of a class of people who do not possess any means of production, is scarcely examined.